Literature, Videos, and CDs

All material is textual unless indicated as video. Many of the items are available on this site, as indicated by the implicit links. "On CD" means that the item is included in the single CD of "Legacy
of R.L. Moore Handouts" available on request from the Legacy
Project. These items can also be sent as printed copy. "JSTOR" provides a link to the full journal article for JSTOR subscribers.

Barrett, Lida K., and Long, B. Vena, "The Moore Method and the Constructivist Theory
of Learning: Was R. L. Moore a Constructivist?" PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(2012), 75-84. "... many mathematicians, including those
who criticize constructivism, revere R. L. Moore as an outstanding teacher of mathematics.... The goal
of this article is to show that Moore's method aligned with a constructivist approach."

Brown, Stephen I., Reconstructing School Mathematics: Problems with Problems and the Real World (Peter Lang, 2001). "What might be viewed as highly suspect (if not downright immoral and debilitating) in the light of present-day prizing of cooperative learning, was a life-enhancing source for an unusually large number of students. In fact, R.L. Moore single-handedly turned out this century's leading set-theoretic topologists." (p. 42) The author was a student of E.E. Moise (Moore PhD, 1947) at the Harvard Graduate School of Education.

Buck, Robert E., "Conjecturing," PRIMUS; 16(June 2006), 97-104. A seminar course for junior-senior mathematics majors is described. The topic is continued fractions, taught by a modified Moore Method, where the focus is on students creating their own mathematics.

______, "The teaching of geometry," 2016. "[I]mplementation of the Common Core State Standards for geometry cannot
be successful until our teachers themselves gain a modern mastery of the subject
that is consistent with these standards."

Garrigus, David. "Creativity in Mathematics." 2009.Video available in three parts
on YouTube
and with additional material on DVD. More than twenty-five influential teachers, top researchers, inventors, and leaders of industry attest to the life changing rewards that began for them in a classroom taught by IBL and the Moore Method.

______., "What is teaching?" Amer. Math. Monthly 101
(1994): 848-855. "I will not, I told them, lecture to you .... They stared at me, bewildered and upset--perhaps even hostile. ... They suspected that I was trying to get away with something, that I was trying to get out of the work I was paid to do. I told them about R.L. Moore, and they liked that, that was interesting. Then I gave them the basic definitions they needed to understand the statements of the first two or three theorems, and said 'class dismissed'. It worked."

Halmos, Paul R., with Renz, Peter, I Want To Be A Mathematician: A Conversation with Paul Halmos. Film by George Csicsery. 2009. Available through the Mathematical Association of America. Description and trailer from Zala Films. "The 1999 interview with Paul Halmos (1916-2006) that forms the backbone of I Want To Be A Mathematician was initiated to gather some comments from Halmos about R.L. Moore for the Educational Advancement Foundation’s R.L Moore Legacy Project."

Kapur, J.N., "Moore method of teaching," in Current Issues in Higher Education in India, (S. Chand, 1975), pp. 203-205. "Today's world needs creative minds and in India the need for such minds is desperate. We should experiment with any method which has a promise of enabling the students to face unfamiliar situations with confidence. The world is so dynamic today that mastery of facts has become secondary to mastery of techniques of acquiring knowledge." Kapur was a professor at Indian Institute of Technology, Kanpur, and Vice-Chancellor of Meerut University.

Kauffman, Robert M., "Some remarks on the Socratic method in mathematics."
On CD.

Legacy of R.L. Moore Project, "Master of the Game," 10-minute
video. Available through theEAF. This is a sample reel, prepared by George Paul Csicsery, for a proposed
new video on Dr. Moore and the Moore Method. It includes excerpts from interviews with
mathematician Paul Halmos and theologian James W. McClendon.

Moore, R.L. "Challenge in the Classroom." Video. (Mathematical Association of America, 1967). Available through the EAF in VHS or DVD format. Transcript. This film features interviews with Moore
and shows him in the classroom. It is the only attempt he made to publicize
his teaching method.

______., "Material and method," Undergraduate Research
in Mathematics: A Report of a Conference Held at Carleton College, Northfield,
Minnesota, June 16 to 23, 1961, Edited by Kenneth O. May and Seymour Schuster,
pp. 9-27.

Yorke, J.A., and Hartl, M.D. "Efficient methods for covering material and Keys to Infinity," Notices of the AMS (June/July 1997): 685-687. PDF version on the AMS web. “Since the roots of the problems described above run so deep, it is imperative that potential solutions (such as the Moore method) be implemented early in students’ careers—and not just for students planning to become mathematicians” (p. 686).

Adamson, I., A General Topology Workbook, ( Springer, 1996). “Highly influenced by the legendary ideas of R. L. Moore, the author has taught several generations of mathematics students with these materials, proving again the usefulness and stimulation of the Moore method” (cover). The author was a student at Princeton 1949-52 (Ph.D. under Emil Artin) and was introduced to the Moore method there by Ralph Fox.

______, A Set Theory Workbook, (Springer, 1997). “The main purpose of this approach is to encourage readers, in the well known educational method of R.L. Moore, to try hard to prove results for themselves” (cover). Review in American Mathematical Monthly on JSTOR.

Asghari, Amir, "Moore and less!," PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(2012), 509–524. "The Moore Method ... implicitly supported me to put into practice an extremely non-traditional
approach [in a multivariable calculus course] where traditions are highly ubiquitous. However, I changed the method to such a great extent
that one can hardly recognize Moore anymore." The author is at Shahid Behesti University, Tehran.

Clark, David M., Euclidean Geometry: A Guided Inquiry Approach, (American Mathematical Society and Mathematical Sciences Research Institute, 2012). Makes use of a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory. Written for an undergraduate axiomatic geometry course, the book is particularly well suited for future secondary school teachers. It covers all the topics listed in the Common Core State Standards for high school synthetic geometry.

______, "Elementary theory of factoring trinomials with integer coefficients over the integers," International Journal of Mathematical Education in Science and Technology 41(2010): 1114-1121.Includes a suggestion for an inquiry-based learning project.

______, "Slip and Slide Method of factoring trinomials with integer coefficients over the integers", International Journal of Mathematics Education in Science and Technology, 43(2012): 548-553.Includes a suggestion for an inquiry-based learning project.

Dydak, Jerzy, and Feldman, Nathan, "Major Theorems on Compactness: a Unified Exposition," Amer. Math. Monthly 99(1992), 220-227. On JSTOR. "[O]ne can easily convert this text to a collection of problems in classes where the Moore Method is used."

Hale, Margie, Essentials of Mathematics: Introduction to Theory, Proof, and the Professional Culture, (Mathematical Association of America, 2003).
From review by Marion Cohen: "I also thoroughly approve of her format, which is consistent with the Moore Method...."

Henle, James, An Outline of Set Theory, (Springer, 1986). "[T]his is a Moore-style text whose proper use depends on the confluence of a patient instructor open to the Moore technique ... with motivated and intelligent students. ... Highly recommended." (Judith Roitman, from review in The Journal of Symbolic Logic, 52(1987), 1048-1049. JSTOR link.) See also The American Mathematical Monthly, 95, 1988, p. 844 (on JSTOR) for Roitman's response to the "vituperative review" by C. Smorynski.

Hodge, Jonathan, and Klima, Richard E., The Mathematics of Voting and Elections: A Hands-On Approach, (American Mathematical Society, 2005). “From a pedagogical standpoint this book was inspired by our involvement in the Legacy of R.L. Moore Project …. When we set out to write this book, we wanted to capture the spirit of a Moore method course, but we also wanted to make sure that the resulting text was accessible to a non-mathematical audience.” (p. x) Online review by Raymond N. Greenwell.

Jolly, R.F., Synthetic Geometry, (Holt, Rinehart and Winston, 1969).Dedicated to R.L. Moore, this text follows a "developmental" course which "entails letting the student develop a body of mathematical material under the guidance of the professor."

"In an effort
to show prospective mathematics majors that mathematics is a vital and beautiful subject, Levine organizes his book around active participation by students in a four-stage scheme for doing mathematics: experimentation, conjecture, proof, and generalization."
-- Review by Robert A. Fontenot. American Mathematical Monthly
108, 2001, 179-182 (on JSTOR).

Mahavier, Wm. S., "Foundation of Mathematics," 2008. A demonstration of the Moore Method by way of video clips, notes, and commentary on a class taught by William S. "Bill" Mahavier at Emory University in 2008.

Marshall, David C.; Odell, Edward; Starbird, Michael, Number Theory Through Inquiry, Mathematical Association of America, 2007. A text "designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). The result of this approach will be that students:

Learn to think independently

Learn to depend on their own reasoning to determine right from wrong

Develop the central, important ideas of introductory number theory on their own."

Moise, Edwin E., Introductory Problem Courses in Analysis and Topology, (Springer, 1982). "The Moore Method is an idea with many fruitful aspects. Let us not throw out the whole idea because it has some difficult points, rather let us search for a wider application of the good aspects. Moise has written an excellent book; it should make it easier for the problem course approach to find a larger place in the undergraduate curriculum." (From the review by Carl C. Cowen in the Amer. Math. Monthly, 91(1984): 528-530.)

Nanzetta, Philip, and Strecker, George E.,
Set Theory and Topology, (Bogden & Quigley, 1971). "Those experienced in the Moore method, I believe, will appreciate and be able to use this book just on the basis of the first two chapters on set theory, but they write their own sets of notes for topology and won't need this one. To those not experienced in the Moore method, I recommend this book as a means of introduction to the method and say, 'try it, you'll like it.'" (R.R. FitzGerald, from review in Amer. Math. Monthly 79(1972), 920-921.)

Schumacher, Carol, Chapter Zero: Fundamental Notions of Abstract Mathematics (Addison-Wesley, 1996).From the blurb: "Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups." Reviewed by Robert A. Fontenot. American Mathematical Monthly 108, 2001, 179-182 (on JSTOR).

Terry, Lawson, Topology: A Geometric Approach, (Oxford University Press, 2003).
"These chapters are written in a very different style, which is motivated in part
by the ideal of the Moore method of teaching topology combined with ideas of VIGRE programs in the US which advocate earlier introduction of seminar and research activities in the advanced undergraduate and graduate curricula" (p. vi).

Personal Experiences as Students and Teachers

Avers, Paul W., "A unit in high school geometry without the textbook," in
Mathematics in the Secondary School Classroom: Selected Readings,
ed. by G.R. Rising and R.A. Wiesen. (Thomas Y. Crowell, 1972), pp. 231-234."Avers' instructional program parallels the work of the nationally known R.L. Moore of the University of Texas. Both are able to get their students emotionally involved with their subject
by taking away their textbooks." (From the editorial introduction, p. 227.)

Foster, James A., and Barnett, M., “Moore formal methods in the classroom: A how-to manual,” in
Teaching and Learning Formal Methods, ed. by M. Hinchey, C. N. Dean. (Morgan Kaufmann, 1996), pp. 79-98.“One of us (Barnett) took courses taught using the method in the departments both of mathematics and of computer sciences while in Austin in the 1980s. We describe the method as it was experienced at that time” (p. 85).

Foster, James A.; Barnett, M.;Van Houten, K.; Sheneman, "(In)Formal Methods: Teaching Program Derivation via the Moore Method,"
Computer Science Education, 6(1), 1995, pp. 67-91. "[T]he students learned the underlying mathematics of program derivation and learned to apply it, by presenting proofs and derivations on a daily basis. Professorial intervention in the classroom was minimal. Our experience has been that students learn otherwise difficult material better, and are better able to put it into practice, with this teaching technique than they would have been able to do in the typical classroom."

Good, Chris, "Teaching by the Moore Method,"
MSOR Connections 6 No. 2(2006), 34-38. The
author, professor of mathematics at the University of Birmingham in
England, describes a first-year course, "Development of Mathematical
Reasoning," which has proven popular and effective for
mathematics students entering the university.

Siegel, Martha J., “Teaching mathematics as a service subject,” in A. G. Howson, et al., eds.,
Mathematics as a Service Subject, ICMI Study Series, (Cambridge University Press, 1988), pp. 75-89. “I have taught, or rather the students have taught themselves, a full syllabus of the course … using a small group discovery method. … In a sort of Moore method approach, the students are given examples to work out with guidance, a form of programmed prodding towards a solution.” (p. 85)

Suppes, P., “Uses of artificial intelligence in computer based instruction,” in
Artificial Intelligence in Higher Education: International Symposium Proceedings, eds. V. Marik, O. Stepankova, Z. Zdrahal, (Springer, 1991). “We adopted a computer version, so to speak, of the famous R.L. Moore method of teaching. ... It is easy to implement such a method in a computer framework. A typical example would be a presentation of fifteen elementary statements about the geometrical relation of betweenness among three points. Students are asked to select no more than five of the statements as axioms and to prove the rest as theorems” (p. 208).

Vick, James W., Review of two topology texts, Amer.
Math. Monthly 116(2009): 373-375."The evidence is clear that the discipline and rigor learned through [the Moore method] have lasting effects. I can still remember the thrill of discovery and the triumph of presentation of a basic theorem as a freshman 47 years ago. ... I will fashion a course [from the text] in which I will include as many of the applications as possible, and on Fridays I will convert the class into a Moore method setting, with students proving theorems from a separate list I have generated." Vick, a professor at the University of Texas at Austin, is a third generation doctoral descendant of Moore.

Bing, RH, "Notes for R H Bing's Plane Topology Course." On CD. A
one-semester undergraduate course started by Bing at Wisconsin and continued
by R.E. Fullerton, S.C. Kleene, and R.F. Williams. The notes were used by
C.B. Allendoerfer at the University of Washington and by W.L. Duren, Jr., at
Tulane University.

______., and Sher, R.B. "B.J. Ball: An appreciation,"
Topology and Its Applications 94(1999), 3-6. On CD.

Green, John W., Presentation at the 2001 Legacy of RL Moore Conference. A principal research biostatistician with DuPont corporation talks about how he went from topology to statistics and "how Dr. Moore’s influence continues in this new career." In the course of a challenging and politically sensitive research position Dr. Green shows how important qualities such as persistence, self-reliance, and clear thinking, as well as a sense of humor, have proven to be valuable lessons he took from Dr. Moore’s classes. (See also his interview with B. Fitzpatrick above.)

Parker, J., R. L. Moore: Mathematician and Teacher (Mathematical
Association of America, 2005). This
is the most comprehensive biography to date and, in contrast to D. R.
Traylor’s 1972 account, it was able to make extensive use of Dr. Moore's
papers and the oral history resource in the Archives
of American Mathematics.

Rogers, J.T., "F.B. Jones -- An appreciation," 1999. On CD.

Rudin, Mary Ellen, "The early works of F.B. Jones," Handbook of
the History of General Topology, Vol. 1. C.Aull and R. Lowen (eds),
Kluwer Academic 1997, 85-96. On CD.

Traylor, D.R., Creative Teaching:
The Heritage of R.L. Moore, University of Houston, 1972. Written
during Dr. Moore’s lifetime but not authorized by him, this account by a
member of the Moore school of mathematics is a major resource for
information about his life and career. The author interviewed early students
and colleagues. Chapters by W. Bane and M. Jones list publications by Moore
and his mathematical descendants.See Paul Halmos's review in Historia Mathematica 1(1974), 188-192.

Zettl, A., "Research on differential equations." On CD. Zettl describes his research but includes a brief biographical account of his family's harrowing escape from a Yugoslavian concentration camp and eventual immigration to the US. Thanks to the Moore Method used in classes that he took, he found his weak mathematics background to be no great disadvantage since he was on the same initial footing as everyone else.

Zitarelli, David, and Bartlow, Thomas L.,"Who was Miss Mullikin?" American Mathematical Monthly 116(2009): 99-114. See The Mathematical Touristsynopsis by Ivars Peterson. Little had been known about Moore's third PhD student Anna Mullikin (1922) who published only one research paper, her dissertation, and became a high school teacher. This article sheds new light on her life and shows how influential her mathematics and her teaching were. For a demonstration of Mullikin's Nautilus, see Demo Collection..

Mentions of Moore and the Moore Method

Ager, Tryg, A., “From interactive instruction to interactive testing,” in Artificial Intelligence and the Future of Testing ed. Roy O. Freedle, (Lawrence Erlbaum Associates, 1990). From the section “Example of finding-axioms: mathematical conjecture”: “VALID has one other exercise type that I would like to discuss. This is by far the most complex type of problem in the course. Based on an idea of R. L. Moore and modified for interactive use in VALID, there are seven ‘finding-axioms’ exercises, of which the following is the simplest” (p. 40).

Dreyfus, T., and Eisenberg, T., "On different facets of mathematical thinking," in The Nature of Mathematical Thinking, eds. R. J. Sternberg, T. Ben-Zeev (Lawrence Erlbaum Associates, 1996), pp. 253-284.
Includes a basically sympathetic account of the Moore Method but finds cooperative learning, viewed as "humanizing Moore," to be more congenial, especially for less motivated students.

Eisenberg, Theodore. “Some of My Pet-Peeves with Mathematics Education,” Mathematics & Mathematics Education: Searching for Common Ground, Michael N. Fried, Tommy Dreyfus (eds.), Springer (2014), 35-44. "My heroes in those days were mathematicians who had a sincere interest in teaching ... [including] R.L. Moore who had this new (to me) way of teaching by pitting student against student in competitive situations. (I did not like the competitive part of Moore's teaching, but one certainly could not argue with his success. And so in mathematics education classes we talked about how to humanize Moore's method.)"

Garrity, T.A. All the Mathematics You Missed: But Need to Know for Graduate School, (Cambridge University Press, 2002), pp. 77-78.
Discusses significance of point-set topology and its changing role in the curriculum over the last 70 years with a special mention of its use by Dr. Moore at the University of Texas.

Knuth, Eric J., "
Secondary School Mathematics Teachers' Conceptions of Proof," Journal for Research in Mathematics Education33, 2002, 379-405. "As undergraduates, do prospective teachers have opportunities to experience and discuss these roles of proof? The Moore Method of teaching, for example, which is used by some mathematicians, provides undergraduate students with just such an experience." (p. 400)

Lucas, J.R.
The Conceptual Roots of Mathematics: An Essay on the Philosophy of Mathematics. (Routledge, 2000).The author, a Fellow of Merton College, Oxford, argues for a form of logicism in which much of mathematics is grounded in transitive relations instead of natural numbers or set theory. After looking at Alfred North Whitehead’s failed attempt to found geometry and topology on a mereological basis, i.e. a theory of whole and part, he considers the transitive relation of ‘being embedded in’ as utilized by R.L. Moore.

Milnor, John,
“Growing up in the old Fine Hall,” in Prospects in Mathematics
ed. Hugo Rossi (American Mathematical Society, 1999), p. 3 “The person who was closest to me in the early years [at Princeton University] was Ralph Fox. … I particularly enjoyed the course in point set topology which he taught by a form of the R. L. Moore method: He told us the theorems and we had to produce the proofs. I can’t think of a better way of learning how to make proofs and how to learn the basic facts of topology – it was a marvelous education.”

Morrel, J.H. “Why lecture? Using alternatives to teach college mathematics,” in Teaching in the 21st Century: Adapting Writing Pedagogies to the College Curriculum, (Routledge (UK), 1999), pp. 29-48. Online purchase http://www.questia.com/
“In order to adapt this [the Moore method where students ‘understood the topics extremely well and had a lot of practice in writing and explaining mathematics’] to an undergraduate setting, in which the time constraints and required syllabi mitigate against the use of such a method, I have used a modification of this approach … ” (p. 38).

Palombi, Fabrizio, and Rota, Gian-Carlo, Indiscrete Thoughts, (Birkhäuser, 1997)."The core of graduate education in mathematics was Dunford's course in linear operators. Everyone who was interested in mathematics at Yale eventually went through the experience, even such brilliant undergraduates as Andy Gleason, McGeorge Bundy, and Murray Gell-Mann. The course was taught in the style of R.L. Moore ..." (p. 29).

Raiffa, H. “Game theory at the University of Michigan, 1948-1952,” in Toward a History of Game Theory ed. E. Roy Weintraub, (Duke University Press, 1993). “I took a course called ‘Foundations of Mathematics’ with Professor Copeland, who taught in the R. L. Moore style: students are challenged to act like mathematicians, to convince themselves and others of the veracity of some plausible conjectures, to concoct starkly simple illuminating counterexamples, to generalize, to speculate, to abstract. No books were used. All the results were proved by the students. … I became hooked. Even though I didn’t know Leonard J. (Jimmy) Savage at the time, he also became enthralled in the same type of teaching program by being forced to act like a mathematician. I decided to become a pure mathematician and pursue a Ph.D. degree” (p. 166).

Ross, Arnold E., "Creativity: Nature or Nurture? A View in Retrospect," in N. Fisher, et al., eds., Mathematicians and Education Reform, 1989-1990, (American Mathematical Society, 1991), pp. 39-84. Ross's early education in the USSR he likens to the Moore Method. Its spirit of “explanation and justification” continued to characterize his own approach to teaching mathematics. However, he mistakenly attributes its origins in the USA to E.H. Moore. (More on this misunderstanding can be found in the 1999 videotaped interview with Ross available at the Archives of American Mathematics.)

Samuelson, Paul A., Inside the Economist's Mind: Conversations with Eminent Economists, (Blackwell, 2006). Robert Aumann on taking real variables from the logician Emil Post at City College in the 1940s: "It's called the Moore method—no lectures, only exercises. It was a very good course." (p. 329)

Selden, A., and Selden, J. “Tertiary mathematics education research and its future,” in Teaching and Learning of Mathematics at University Level: An ICMI Study, ed. Derek Holton, (Springer, 2001), pp. 255-274.
A section on the Moore Method suggests that courses making use of it “could provide interesting opportunities for research in mathematics education.”

Shier, D.R., and Wallenius, K.T. Applied Mathematical Modeling: A Multidisciplinary Approach, (CRC Press, 1999). “The modeling approach in applied mathematics has much in common with the discovery methods used in pure mathematics, such as the famous R. L. Moore approach” (p. 14).

Szenberg, M., and Ramrattan, L.B.,eds.,
Collaborative Research in Economics: The Wisdom of Working Together, (Springer, 2017). “Collaboration is formed from the desire to follow or imitate the leader. ... The mathematic discipline provides such an example in regard to the Moore method.” (Introduction by the editors, pp. 15-16.)

Winkler, P. Mathematical Puzzles: A Connoisseur's Collection, (A K Peters, Ltd., 2004). The author comments on the “figure 8s in the plane puzzle" that he “heard it attributed to the late, great topologist R. L. Moore.”

Finkel, Donald L., Teaching with Your Mouth Shut, (Boynton/Cook, 2000)."The teacher, then, attempts to create a blueprint for learning by keeping her mouth shut and instead designing an environment for her students with the following three features: (1) The teacher presents an overall problem-to-be-solved, which is broken down into smaller problems that build on each other …. (2) The teacher creates a blueprint for a ‘whole’ experience …. (3) She reconfigures the classroom so that she is ‘out of the middle’ ….” (p. 108).
"In sum, the teacher refuses to govern the students in their inquiry because he wants the students to learn how to govern themselves” (p.115).

Wilder, Raymond L., "The Role of Intuition," Science, NS 156(1967), 605-610. On JSTOR. "Intuition plays a basic and indispensable role in mathematical research and in modern teaching methods."

Woodruff, Paul, Reverence: Renewing a Forgotten Virtue, (Oxford University Press, 2001). "A silent teacher need not treat lofty subjects. You think it a trivial fact that seven plus five equals twelve, but one may stand in awe of it nevertheless (as has more than one great philosopher). With awe or without, a teacher is well advised to be quiet from time to time about even the most ordinary facts, so that students may have the freedom to make those facts their own." (On "The Silent Teacher," p. 189.)